Please answer all questions with detailed explanation.

Asia Furnishing is a retailer of modular toilet products. Currently, the lead time for one of the products, the toilet door, is relatively high, at 5 weeks. The average demand for toilet doors is 200 per week. The standard deviation of demand during the lead time is 85 doors. The store plans to provide a service level of 99 per cent.

(a) The store is looking for another supplier who can supply the doors in one week at the same price. Analyse how much safety stock can be reduced by moving to the new supplier without reducing the 99 per cent cycle-service level. (15 marks)

(b) The store hired a new manager who insists on using a probability distribution for the lead time of supply, instead of a fixed lead time. Based on the historical data from the present supplier, she estimated that the standard deviation of lead time is 1 week. How will the amount of safety stock change after including this information? What should be the reorder level for the store? (10 marks)